Density Word Problem

[piggykid1]

A ship has a volume of 85,000 cubic tons. The density of steel is 8 grams/milliliter and air is 0.001 grams/milliliter, what percent of the ship must be air to float in the water. ("The water" is 1 gram/milliliter)

 

Thank you very much!

 

Also I have to show work so a brief explanation would be great!

[Sensei]

Cubic ton is different unit than the rest mentioned

http://en.wikipedia.org/wiki/Cubic_ton

 

g/mL is simply equal to g/cm³

 

Air has approximately 1.29 g/L at STP not 1 g/L

 

So you should start from unification of units.

Edited December 12, 2014 by Sensei

[imatfaal]

Cubic ton is different unit than the rest mentioned

http://en.wikipedia.org/wiki/Cubic_ton

 

g/mL is simply equal to g/cm³

 

Air has approximately 1.29 g/L at STP not 1 g/L

 

So you should start from unification of units.

 

At STP it is 1.2754 kg/m3. In these circumstances RTP might be better tho - and the water will be very humid (RTP and STP figures are dry) which will take the figure even closer to that which is given. But rather than adjust for temp, pressure, and humidity I would heartily recommend using the figure given in the question.

 

Agree completely on the units - as someone who does shipping calcs for a living I would convert everything to kg (maybe metric tonnes) and metres. And as a commercial man I would mention that the ship in the question won't be able to carry any cargo - which kind of removes the point of the ship in the first place (in shipping terms zero deadweight).

[Sensei]

 

At STP it is 1.2754 kg/m3. In these circumstances RTP might be better tho - and the water will be very humid (RTP and STP figures are dry) which will take the figure even closer to that which is given. But rather than adjust for temp, pressure, and humidity I would heartily recommend using the figure given in the question.

 

I used this website as reference:

http://en.wikipedia.org/wiki/Density_of_air

And it has 1.2922 g/L at 0 C, 101.325 kPa

In any case, it's 15-30% higher than OP value 1 g/L.

Edited December 12, 2014 by Sensei

[imatfaal]

 

I used this website as reference:

http://en.wikipedia.org/wiki/Density_of_air

And it has 1.2922 g/L at 0 C, 101.325 kPa

In any case, it's 15-30% higher than OP value 1 g/L.

 

With respect you didn't use the resource properly (the figure at STP is clearly shown on your cited page) - and in homework help that is poor form.

 

STP as defined by IUPAC is 0 deg C and 100 kPa - you gave the density at 1 atm - not 100kPa.

[Sensei]

Right, there is 1.3% difference between these two values.

Either

[math]\frac{p_0}{p_1}=\frac{101325}{100000}=1.01325 = 1.3\% difference[/math]

and

[math]\frac{m_0}{m_1}=\frac{1.2922}{1.2754}=1.01317 = 1.3\% difference[/math]

 

So I don't know what for somebody is giving me negative??

Edited December 12, 2014 by Sensei

[DevilSolution]

They're dense